There are so many different practices that people call yoga. What is the most authentic in terms of being supported by Hindu scriptures?
The term Yoga is formed from the dhatu 'Yuj'. Panini Dhatupad says following for the meaning of dhatu 'Yuj'.
Yuj samadhau: Samadhi. So, yoga means attaining Samadhi state/ fourth/ turiya state. So, any path that can lead to Turiya/ Samadhi state can be called Yoga.
Yuj yoge: Union. So, when something is united it is called Yoga. When two atoms are united then it is also called yoga between two atoms. Similarly Union of individual with God/ Universe is Yoga.
Yuj samyamane: Censure. Censuring thought waves in mental pond to see the self within clearly. It is like cleaning the mental mirror to see our own self.
So, any path that leads one to Samadhi or Union with something or stopping of thought waves can be called Yoga. As there can be many paths for this so there are many Yogas.
The 18 Chapters of Bhagvad Gita are classified as Yoga. It is because single chapter can lead one to the Turiya state or Union with something. They are:
Chapter 1 : Visada Yoga
Chapter 2 : Sankhya Yoga
Chapter 3 : Karma Yoga
Chapter 4 : Jnana Yoga
Chapter 5 : Karma Vairagya Yoga
Chapter 6 : Abhyasa Yoga
Chapter 7 : Paramahamsa Vijnana Yoga
Chapter 8 : Aksara-Parabrahman Yoga
Chapter 9 : Raja-Vidya-Guhya Yoga
Chapter 10 : Vibhuti-Vistara-Yoga
Chapter 11 : Visvarupa-Darsana Yoga
Chapter 12 : Bhakti Yoga
Chapter 13 : Ksetra-Ksetrajna Vibhaga Yoga
Chapter 14 : Gunatraya-Vibhaga Yoga
Chapter 15 : Purusottama Yoga
Chapter 16 : Daivasura-Sampad-Vibhaga Yoga
Chapter 17 : Sraddhatraya-Vibhaga Yoga
Chapter 18 : Moksa-Opadesa Yoga
Among these Karma Yoga, Jnana Yoga and Bhakti Yoga are most popular in todays time. Some Yoga fall in sub branches of these Yogas.
As the name implies it is eight limbed Yoga. The eight limbs are:
Yam, Niyam, Asana, Pranayama, Pratyahara, Dharana, Dhyana and Samadhi.
Patanjali in 'Patanjali Yoga Sutras' describes this Yoga. Several other Puranas also describe it. As in the eight limbs the final limb is 'Samadhi'. So Ashtanga Yogas main goal is to reach to Samadhi. But todays people don't even think about attaining Samadhi. They just practice Asana (specific position) and Pranayama (breathing techniques). And people now think main goal of Yoga is for removing diseases.
Kundalini Yoga is also somewhat popular. It is also scriptual based as I discuss in my answer here.
Uniting the Kundalini (Shakti) with Shiva sitting in Sahasrara by crossing 6 chakras in the path and thus attaining Kaivalya is Kundalini Yoga.
It is based on six limbs which are:
asana, pranayama, pratyahara, dharana, dhyana and samādhi.
Shat-Kriyas applied for purification of body are
Netī, Dhautī, Naulī, Basti, Kapālabhātī, Trāṭaka
They are related with fully cleansing body including internal organs, 'Trataka' is used to gain extreme concenteration and thus leading to Samadhi. It was discovered by Guru Gorakhnath, Matsendra Nath and Other Nava Naths. So, mostly people of Nath Sampradaya Practice this.
It is related with controlling of mind. It is also described in Bhagvad Gita chapter 6. For eg verse 6 says:
"A yogi should always try to concentrate his mind, retiring into solitude and living alone, having subdued his mind and body and got rid of his desires and possessions." For more details see answer here.
It is advanced Raja Yoga mixed with Pranayama exercises. See answer here. for more details.
There can be other several Yogas like Mantra Yoga (attaining union through mantras), Tantra Yoga, Yantra Yoga and so on many other Yogas. As there can be infinite paths to reach Supreme or to Unite with something, so there are infinite Yogas. One should choose path/paths which is/are suitable for him and finally be united with what he desires